Consider the following gas phase reaction being carried out in a...

For the given gas phase reaction:

$2A(g) \rightarrow 4B(g) + C(g)$

Let the initial pressure of $A(g)$ be $P_0$.

At $t = 0$: $P_A = P_0$, $P_B = 0$, $P_C = 0$

At $t = t$: $P_A = P_0 - 2p$, $P_B = 4p$, $P_C = p$

Total pressure at time $t$, $P_t = P_0 - 2p + 4p + p = P_0 + 3p$

At $t = \infty$, the reaction is complete, so $P_A = 0 \Rightarrow 2p = P_0 \Rightarrow p = \dfrac{P_0}{2}$

Total pressure at $t = \infty$, $P_{\infty} = 4\left(\dfrac{P_0}{2}\right) + \dfrac{P_0}{2} = \dfrac{5P_0}{2}$

Given $P_{\infty} = 600$ mm Hg:

$\dfrac{5P_0}{2} = 600 \Rightarrow P_0 = 240$ mm Hg

At $t = 30$ min, $P_t = 300$ mm Hg:

$P_0 + 3p = 300$

$240 + 3p = 300 \Rightarrow 3p = 60 \Rightarrow p = 20$ mm Hg

The pressure of $C(g)$ at $30$ minutes is $p = 20$ mm Hg.

Answer: $20$